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Differential Geometry From A Singularity Theory Viewpoint
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Book Synopsis Differential Geometry From A Singularity Theory Viewpoint by : Shyuichi Izumiya
Download or read book Differential Geometry From A Singularity Theory Viewpoint written by Shyuichi Izumiya and published by World Scientific. This book was released on 2015-10-29 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Geometry from a Singularity Theory Viewpoint provides a new look at the fascinating and classical subject of the differential geometry of surfaces in Euclidean spaces. The book uses singularity theory to capture some key geometric features of surfaces. It describes the theory of contact and its link with the theory of caustics and wavefronts. It then uses the powerful techniques of these theories to deduce geometric information about surfaces embedded in 3, 4 and 5-dimensional Euclidean spaces. The book also includes recent work of the authors and their collaborators on the geometry of sub-manifolds in Minkowski spaces.
Book Synopsis Differential Geometry Of Curves And Surfaces With Singularities by : Masaaki Umehara
Download or read book Differential Geometry Of Curves And Surfaces With Singularities written by Masaaki Umehara and published by . This book was released on 2021 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book provides a unique and highly accessible approach to singularity theory from the perspective of differential geometry of curves and surfaces. It is written by three leading experts on the interplay between two important fields - singularity theory and differential geometry. The book introduces singularities and their recognition theorems, and describes their applications to geometry and topology, restricting the objects of attention to singularities of plane curves and surfaces in the Euclidean 3-space. In particular, by presenting the singular curvature, which originated through research by the authors, the Gauss-Bonnet theorem for surfaces is generalized to those with singularities. The Gauss-Bonnet theorem is intrinsic in nature, that is, it is a theorem not only for surfaces but also for 2-dimensional Riemannian manifolds. The book also elucidates the notion of Riemannian manifolds with singularities. These topics, as well as elementary descriptions of proofs of the recognition theorems, cannot be found in other books. Explicit examples and models are provided in abundance, along with insightful explanations of the underlying theory as well. Numerous figures and exercise problems are given, becoming strong aids in developing an understanding of the material. Readers will gain from this text a unique introduction to the singularities of curves and surfaces from the viewpoint of differential geometry, and it will be a useful guide for students and researchers interested in this subject"--
Book Synopsis Differential Geometry from the Viewpoint of Lagrangian Or Legendrian Singularity Theory by : Shyuichi Izumiya
Download or read book Differential Geometry from the Viewpoint of Lagrangian Or Legendrian Singularity Theory written by Shyuichi Izumiya and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry from the Viewpoint of Lagrangian Or Legendrian Singularity Theory by :
Download or read book Differential Geometry from the Viewpoint of Lagrangian Or Legendrian Singularity Theory written by and published by . This book was released on 2005 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry Of Curves And Surfaces With Singularities by : Masaaki Umehara
Download or read book Differential Geometry Of Curves And Surfaces With Singularities written by Masaaki Umehara and published by World Scientific. This book was released on 2021-11-29 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unique and highly accessible approach to singularity theory from the perspective of differential geometry of curves and surfaces. It is written by three leading experts on the interplay between two important fields — singularity theory and differential geometry.The book introduces singularities and their recognition theorems, and describes their applications to geometry and topology, restricting the objects of attention to singularities of plane curves and surfaces in the Euclidean 3-space. In particular, by presenting the singular curvature, which originated through research by the authors, the Gauss-Bonnet theorem for surfaces is generalized to those with singularities. The Gauss-Bonnet theorem is intrinsic in nature, that is, it is a theorem not only for surfaces but also for 2-dimensional Riemannian manifolds. The book also elucidates the notion of Riemannian manifolds with singularities.These topics, as well as elementary descriptions of proofs of the recognition theorems, cannot be found in other books. Explicit examples and models are provided in abundance, along with insightful explanations of the underlying theory as well. Numerous figures and exercise problems are given, becoming strong aids in developing an understanding of the material.Readers will gain from this text a unique introduction to the singularities of curves and surfaces from the viewpoint of differential geometry, and it will be a useful guide for students and researchers interested in this subject.
Book Synopsis Curves and Singularities by : J. W. Bruce
Download or read book Curves and Singularities written by J. W. Bruce and published by Cambridge University Press. This book was released on 1992-11-26 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors take a novel approach by casting the theory into a new light, that of singularity theory. The second edition of this successful textbook has been thoroughly revised throughout and includes a multitude of new exercises and examples. A new final chapter has been added that covers recently developed techniques in the classification of functions of several variables, a subject central to many applications of singularity theory. Also in this second edition are new sections on the Morse lemma and the classification of plane curve singularities. The only prerequisites for students to follow this textbook are a familiarity with linear algebra and advanced calculus. Thus it will be invaluable for anyone who would like an introduction to the modern theories of catastrophes and singularities.
Book Synopsis Handbook of Geometry and Topology of Singularities VI: Foliations by : Felipe Cano
Download or read book Handbook of Geometry and Topology of Singularities VI: Foliations written by Felipe Cano and published by Springer Nature. This book was released on with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Theory of Singular Phenomena in Partial Differential Equations by : Jean Pierre Bourguignon
Download or read book Geometric Theory of Singular Phenomena in Partial Differential Equations written by Jean Pierre Bourguignon and published by Cambridge University Press. This book was released on 1998-05-28 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers together papers from a workshop held in Cortona, Italy. The contributions come from a group of outstanding mathematicians and together they cover the most recent advances in the geometric theory of singular phenomena of partial differential equations occurring in real and complex differential geometry. This volume will be of great interest to all those whose research interests lie in real and complex differential geometry, partial differential equations, and gauge theory.
Book Synopsis Applications of singularity theory of differential equations and differential geometry by : Masatomo Takahashi
Download or read book Applications of singularity theory of differential equations and differential geometry written by Masatomo Takahashi and published by . This book was released on 2009 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry and Lie Groups by : Jean Gallier
Download or read book Differential Geometry and Lie Groups written by Jean Gallier and published by Springer. This book was released on 2021-08-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications. Starting with the matrix exponential, the text begins with an introduction to Lie groups and group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the construction of manifolds from gluing data is particularly relevant to the reconstruction of surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second part of the book, which focuses on Riemannian geometry. Chapters on Riemannian manifolds encompass Riemannian metrics, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics. Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume Differential Geometry and Lie Groups: A Second Course.
Author :Vladimir Igorevich Arnolʹd Publisher :Cambridge University Press ISBN 13 :9780521422802 Total Pages :88 pages Book Rating :4.4/5 (228 download)
Book Synopsis The Theory of Singularities and Its Applications by : Vladimir Igorevich Arnolʹd
Download or read book The Theory of Singularities and Its Applications written by Vladimir Igorevich Arnolʹd and published by Cambridge University Press. This book was released on 1991-05-31 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, which is based on lectures given in Pisa under the auspices of the Accademia Nazionale dei Lincei, the distinguished mathematician Vladimir Arnold describes those singularities encountered in different branches of mathematics. He avoids giving difficult proofs of all the results in order to provide the reader with a concise and accessible overview of the many guises and areas in which singularities appear, such as geometry and optics; optimal control theory and algebraic geometry; reflection groups and dynamical systems and many more. This will be an excellent companion for final year undergraduates and graduates whose area of study brings them into contact with singularities.
Book Synopsis Theory of Singularities and Its Applications by : Vladimir Igorevich Arnolʹd
Download or read book Theory of Singularities and Its Applications written by Vladimir Igorevich Arnolʹd and published by . This book was released on 1990 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of singularities lies at the crossroads between those branches of mathematics which are the most abstract and those which are the most applied. Algebraic and differential geometry and topology, commutative algebra and group theory are as intimately connected to singularity theory as are dynamical systems theory, control theory, differential equations, quantum mechanical and quasi-classical asymptotics, optics, and functional analysis. This collection of papers incorporates recent results of participants in the editor's ongoing seminar in singularity theory, held in the Mechanics and.
Book Synopsis Differential Geometry Curves Surfaces by :
Download or read book Differential Geometry Curves Surfaces written by and published by . This book was released on 2021-12-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Singularity Theory and its Applications by : David Mond
Download or read book Singularity Theory and its Applications written by David Mond and published by Springer. This book was released on 1991-07-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A workshop on Singularities, Bifurcation and Dynamics was held at Warwick in July 1989 as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory, and applications in the sciences. The papers are orginal research, stimulated by the symposium and workshops: All have been refereed, and none will appear elsewhere. The main topic, deformation theory, is represented by several papers on descriptions of the bases of versal deformations, and several more on descriptions of the generic fibres. Other topics include stratifications, and applications to differential geometry.
Book Synopsis New Developments in Singularity Theory by : Dirk Wiersma
Download or read book New Developments in Singularity Theory written by Dirk Wiersma and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters. The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.
Book Synopsis Differential Geometry of Singular Spaces and Reduction of Symmetry by : Jędrzej Śniatycki
Download or read book Differential Geometry of Singular Spaces and Reduction of Symmetry written by Jędrzej Śniatycki and published by Cambridge University Press. This book was released on 2013-06-13 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete presentation of the theory of differential spaces, with applications to the study of singularities in systems with symmetry.
Book Synopsis Introduction to Differential Geometry by : Joel W. Robbin
Download or read book Introduction to Differential Geometry written by Joel W. Robbin and published by Springer Nature. This book was released on 2022-01-12 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.
